Consider r= cos2theta in polar form.

I understand that if you want the area of one loop you would integrate ( o.5r^2) between -pi/4 to pi/4.

But what is the interpretation of integrating between -pi to pi?

I know it is something to do with r becoming negative but what am i working out in this case?

Also do negative r areas cancel out positive r areas like they do in cartesian?